In Minkowski superspace, the linearised higher-spin super-Cotton tensor [1]}, [2]} is
\(\mathfrak {W}_{\alpha _1 \dots \alpha _n}(H) =\Big ( -\frac{{\rm i}}{2}\Big )^nD^{\beta _1} D_{(\alpha _1} \dots D^{\beta _n} D_{\alpha _n)} H_{\beta _1 \dots \beta _n}~,\) 
